# For real gases, how does a change in pressure affect the ratio of PV to nRT?

Jul 14, 2017

It depends on the gas. The ratio of $P V$ to $n R T$ is the compressibility factor $Z$:

$Z = \frac{P V}{n R T}$

• When $Z > 1$, the molar volume of the gas is larger than predicted by the ideal gas law, so the gas's repulsive intermolecular forces dominate.

• When $Z < 1$, the molar volume of the gas is smaller than predicted by the ideal gas law, so the gas's attractive intermolecular forces dominate.

• When $Z = 1$, the gas is ideal.

In principle, higher pressures (and lower temperatures) should make the gas behave more like a real gas (interacting, "sticky" particles).

But higher pressures alone don't give rise to a clear relationship with $Z$.

You can see that at higher temperatures, the curve for ${\text{N}}_{2}$ converges upon $Z = 1$ across a large range of pressures, demonstrating that very high temperatures give rise to an ideal gas. Having low pressures as well makes it easier to accomplish that feat.